Problem: A circle has a radius of ${5}$. An arc in this circle has a central angle of $162^\circ$. What is the length of the arc? Either enter an exact answer in terms of $\pi$ or use $3.14$ for $\pi$ and enter your answer as a decimal. ${162^\circ}$ ${5}$
Answer: First, calculate the circumference of the circle. ${162^\circ}$ ${5}$ ${10\pi}$ ${c} = 2\pi r = 2\pi ({5}) = {10\pi}$ The ratio between the arc's central angle ${\theta}$ and $360^\circ$ is equal to the ratio between the arc length ${s}$ and the circle's circumference ${c}$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{162}^\circ}{360^\circ} = \dfrac{{s}}{{{10\pi}}}$ $\dfrac{9}{20} = \dfrac{{s}}{{10\pi}}$ $\dfrac{9}{20} \times {10\pi} = {s}$ $\dfrac{9}{2}\pi = {s}$ ${162^\circ}$ ${5}$ ${10\pi}$ ${\dfrac{9}{2}\pi}$